Sheila is a wildlife biologist. At the beginning of each year, she tracks the wild turkey and white-tail deer population in the game reserve where she works. At the first year Sheila counted $12$ wild turkeys, and their number increases by approximately $40\%$ each year. At the first year Sheila counted $18$ white-tail deer, and their number increases by $10$ additional deer per year. What is the first year in which Sheila counts more turkeys than deer?
Notice that the turkey cumulative total grows exponentially while the deer cumulative total grows linearly. This means the turkey cumulative total is bound to exceed the deer cumulative total at some point. Let's start calculating the cumulative total for each animal to see when that happens. Year Turkeys Deer (Multiply by $1.4$ each year.) (Add $10$ each year.) $1$ $12$ $18$ $2$ $17$ $28$ $3$ $24$ $38$ $4$ $33$ $48$ $5$ $46$ $58$ $6$ $65$ $68$ $7$ $90$ $78$ Sheila's cumulative count of the turkeys first exceed the cumulative count of the deer in the $7^\text{th}$ year after she started counting.